Global potential energy surfaces (PESs) for the 1 2A' and 1 2A″ states of the C2N system responsible for the N(4Su) + C2(a 3Πu) → CN(X 2Σ+) + C(3Pg) reaction are mapped using compressed-state multistate pair-density functional theory (CMS-PDFT), which is a multi-state version of multiconfiguration pair-density functional theory (MC-PDFT). Calculations are also performed at selected geometries by explicitly correlated multireference configuration interaction with quadruple corrections, MRCI-F12+Q, and the comparison of the two sets of calculations shows that CMS-PDFT describes the globally reactive PESs well, including the bond-breaking asymptotes. We conclude that CMS-PDFT is an efficient method for constructing PESs for strongly correlated reactive systems. The PESs for producing CN + C are found to be barrierless and proceed through intermediate complexes. The CMS-PDFT PESs were fitted with a neural network method, and quasiclassical trajectories were computed on the resulting analytic PESs. These trajectories predict that the reaction produces vibrationally excited CN.